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Investigating Spearman’s hypothesis by means of multigroup confirmatory factor analysis
 Multivariate Behavioral Research
, 2000
"... Differences between blacks and whites on cognitive ability tests have been attributed to a fundamental difference between these groups in general intelligence (or g, as it is denoted). The hypothesized difference in g gives rise to Spearman’s hypothesis, which states that the differences in the mean ..."
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Cited by 17 (6 self)
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Differences between blacks and whites on cognitive ability tests have been attributed to a fundamental difference between these groups in general intelligence (or g, as it is denoted). The hypothesized difference in g gives rise to Spearman’s hypothesis, which states that the differences in the means of the tests are related to the tests ’ factor loadings on g. Jensen has investigated this hypothesis by correlating differences in means and tests ’ g loadings. The aim of the present article is to investigate BW differences using multigroup confirmatory factor analysis. The advantages of multigroup confirmatory factor analysis over Jensen’s test of Spearman’s hypothesis are discussed. A published data set is analyzed. Strict factorial invariance is tested and judged to be tenable. Various models are tested, which do and do not incorporate g. It is observed that it is difficult to distinguish between several hypotheses, including and excluding g, concerning group differences. The inability to distinguish between competing models using multigroup confirmatory factor analysis makes it difficult to draw clear conclusions about the exact nature of blackwhite differences in cognitive abilities. The implications of the results for Jensen’s test of Spearman’s hypothesis are discussed.
The TETRAD Project: Constraint Based Aids to Causal Model Specification
 MULTIVARIATE BEHAVIORAL RESEARCH
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Investigating group differences on cognitive tests using Spearman’s hypothesis: An evaluation of Jensen’s method
 Multivariate Behavioral Research
, 2001
"... Jensen has posited a research method to investigate group differences in cognitive tests. This method consists of first extracting a general intelligence factor by means of exploratory factor analysis. Secondly, similarity of factor loadings across groups is evaluated in an attempt to ensure that th ..."
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Cited by 6 (2 self)
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Jensen has posited a research method to investigate group differences in cognitive tests. This method consists of first extracting a general intelligence factor by means of exploratory factor analysis. Secondly, similarity of factor loadings across groups is evaluated in an attempt to ensure that the same constructs are measured. Finally, the correlation is computed between the loadings of the tests on the general intelligence factor and the mean differences between groups on the tests. This part is referred to as a test of “Spearman’s Hypothesis”, which essentially states that differences in g account for the main part of differences in observed scores. Based on the correlation, inferences are made with respect to group differences in general intelligence. The validity of these inferences is investigated and compared to the validity of inferences based on multigroup confirmatory factor analysis. For this comparison, population covariance matrices are constructed which incorporate violations of the central assumption underlying Jensen’s method concerning the existence of g and/or violations of Spearman’s Hypothesis. It is demonstrated that Jensen’s method is quite insensitive to the violations. This lack of specificity is observed consistently for all types of violations introduced in the present study. Multigroup confirmatory factor analysis emerges as clearly superior to Jensen’s method.
The modelsize effect on traditional and modified tests of covariance structures
 Structural Equation Modeling
, 2007
"... According to Kenny and McCoach (2003), chisquare tests of structural equation models produce inflated Type I error rates when the degrees of freedom increase. So far, the amount of this bias in large models has not been quantified. In a Monte Carlo study of confirmatory factor models with a range o ..."
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Cited by 5 (4 self)
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According to Kenny and McCoach (2003), chisquare tests of structural equation models produce inflated Type I error rates when the degrees of freedom increase. So far, the amount of this bias in large models has not been quantified. In a Monte Carlo study of confirmatory factor models with a range of 48 to 960 degrees of freedom it was found that the traditional maximum likelihood ratio statistic, TML, overestimates nominal Type I error rates up to 70 % under conditions of multivariate normality. Some alternative statistics for the correction of modelsize effects were also investigated: the scaled Satorra–Bentler statistic, TSC; the adjusted Satorra–
Simple second order chisquare correction. Retrieved from Mplus website: http:// www.statmodel.com/download/WLSMV_new_chi21.pdf Bandalos
 In R. C. Serlin (Series
, 2010
"... In this note we describe the second order correction for the chisquare statistic implemented in Mplus Version 6 with the estimators WLSMV/ULSMV and MLMV. Prior to Version 6 the second order correction in Mplus for the chisquare statistics is based on a Satterthwaite (1941) type correction, see also ..."
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Cited by 4 (2 self)
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In this note we describe the second order correction for the chisquare statistic implemented in Mplus Version 6 with the estimators WLSMV/ULSMV and MLMV. Prior to Version 6 the second order correction in Mplus for the chisquare statistics is based on a Satterthwaite (1941) type correction, see also
Effective connectivity of fMRI data using ancestral graph theory: Dealing with missing regions
"... Most of the current methods to assess effective connectivity from functional magnetic resonance imaging (fMRI) rely on the assumption that all relevant brain regions are entered into the analysis. If this assumption is untenable, which we believe is most often the case, then spurious connections bet ..."
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Most of the current methods to assess effective connectivity from functional magnetic resonance imaging (fMRI) rely on the assumption that all relevant brain regions are entered into the analysis. If this assumption is untenable, which we believe is most often the case, then spurious connections between brain regions can appear. In this paper we propose to use an ancestral graph to model connectivity, which provides a way to avoid spurious connections. The ancestral graph is determined from trialbytrial variation and not from the time series. A random effects model is defined for ancestral graphs which allows for individual differences. The framework of local misspecification in the random effects model is used, which allows for modeling errors in connections and brain regions. The framework of local misspecification additionally provides a test on parameters in the graph which is robust against model misspecification. The test can be used to find differences in connection strength between, for example, conditions. Monte Carlo simulations show that the ancestral graph is appropriate to use even with modeling errors. To assess the accuracy further, the proposed method was applied to real fMRI data to determine how brain regions interact during speech monitoring.
Diagnosis for Covariance Structure Models by Analyzing the Path
"... When a covariance structure model is misspecified, parameter estimates will be affected. It is important to know which estimates are systematically affected and which are not. The approach of analyzing the path is both intuitive and informative for such a purpose. Different from path analysis, analy ..."
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When a covariance structure model is misspecified, parameter estimates will be affected. It is important to know which estimates are systematically affected and which are not. The approach of analyzing the path is both intuitive and informative for such a purpose. Different from path analysis, analyzing the path uses path tracing and elementary numerical analysis to identify affected parameters when a 1way or 2way arrow in a path diagram is omitted. It not only characterizes how a misspecification affects model parameters but also facilitates a good understanding of the relation among different parts of the model. This article introduces and studies this technique and, for commonly used models, provides detailed analysis to identify the directions of change for various model parameters. Examples based on real data show that the technique of analyzing the path can reliably predict the direction of change in parameter estimates even when the true model is unknown. Conditions that interfere with the results are also discussed and advice is provided for its proper application. Structural equation modeling (SEM) plays an important role in understanding the relations among multivariate data (Bollen, 1989; MacCallum & Austin, 2000). In a typical application of SEM, one has a substantively justified model, which is quite likely unacceptable when statistically tested. The model modification
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"... On the relationship between sources of within and betweengroup differences and measurement invariance in the common factor model ..."
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On the relationship between sources of within and betweengroup differences and measurement invariance in the common factor model
TEACHER’S CORNER Structural Equation Modeling With the sem Package in R
"... R is free, opensource, cooperatively developed software that implements the S statistical programming language and computing environment. The current capabilities of R are extensive, and it is in wide use, especially among statisticians. The sem package provides basic structural equation modeling f ..."
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R is free, opensource, cooperatively developed software that implements the S statistical programming language and computing environment. The current capabilities of R are extensive, and it is in wide use, especially among statisticians. The sem package provides basic structural equation modeling facilities in R, including the ability to fit structural equations in observed variable models by twostage least squares, and to fit latent variable models by full information maximum likelihood assuming multinormality. This article briefly describes R, and then proceeds to illustrate the use of the tsls and sem functions in the sem package. The article also demonstrates the integration of the sem package with other facilities available in R, for example for computing polychoric correlations and for bootstrapping. R (Ihaka & Gentleman, 1996; R Development Core Team, 2005) is a free, opensource, cooperatively developed implementation of the S statistical programming language and computing environment (Becker, Chambers, & Wilks, 1988;